Question

Find the square root of $529$ using long division method

Answer 1

Step $1$ : We write $529$ as $5\overline{29}$ by grouping the numbers in pairs, starting from the right end. (i.e. from the units place ).
Step $2$ : Find the number whose square is less than (or equal to) $5$. Here it is $2$.
Step $3$ : Put $2$ on the top, and also write $2$ as a divisor as shown.
Step $4$ : Multiply $2$ on the top with the divisor $2$ and write $4$ under $5$ and subtract. The remainder is $1$.
Step $5$ : Bring down the pair $29$ by the side of the remainder $1$, yielding $129$.
Step $6$ : Double $2$ and take the resulting number $4$. Find that number $n$ such that $4n\times n$ is just less than or equal to $129$.
For example: $42\times 2=84$; and $43\times 3=129$ and so $n=3$.
Step $7$ : Write $43$ as the next divisor and put $3$ on the top along with $2$. Write the product $43\times 3=129$ under $129$ and subtract. Since the remainder is $0$, the division is complete. Hence $\sqrt{529}=23$.